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360 Reviews. 

The arrangement pointed out in our correspondent's letter is highly in- 
genious, and would no doubt meet the exigencies of the case; but the 
additional labour would be considerable, inasmuch as the column A,ti 
would have to be calculated afresh at each valuation, on account of the 
bonus additions, — a circumstance which appears to have escaped our 
correspondent's observation. — Ed. A.M.~\ 



Epidemiological Society. — We have received from the Honorary Secre- 
taries of the Epidemiological Society the rules and regulations of that 
Society, with an exposition of its objects; also the printed queries issued 
by the Small-pox and Vaccination Committees, and those of the common 
Lodging-house Committee. In our next Number we will lay before our 
readers the more prominent questions contained in the papers sent to us, 
which came too late to be further noticed at present. The establishment of 
a Society amongst the medical profession for inquiries into the numerous 
topics affecting sanatory and vital statistics, on which the experience and 
talent in that profession can, if well directed, throw so much light, is a 
circumstance of considerable interest; and we think that such a Society 
well deserves the support and active assistance of all who desire to throw 
aside theories based on mere idle speculations, and to draw their conclu- 
sions only from the comparison of, and reasoning upon, well-established 
facts. In the meantime we refer our readers to Dr. Babington's letter in 
our last Number for a brief epitome of the plan of the Society, and the 
intentions of its founders. 



REVIEWS OF NEW WORKS. 

Industrial Investment and Emigration : being a Treatise on Benefit 
Building Societies, and on the general principles of Associations for 
Land Investment and Colonization. With an Appendix on Com- 
pound Interest, Tontines, and Life Assurance. By Arthur Scratch- 
ley, M. A., Actuary to the Western Life Assurance Society. Second 
Edition, much enlarged. London: J. W. Parker, West Strand. 1851. 

The labours of Mr. Scratchley in this now widely-extended field are 
familiar to the public. It is to him, indeed, that the system upon which 
building societies are founded, mainly owes its purification from the most 
dangerous fallacies, and a much more perfect organization at the present 
day. In the first edition of his work, published in 1849, Mr. Scratchley 
laid down the principles upon which building societies must be based to 
have any chance of ultimate success, and exposed very completely the all 
but universal departure from those principles which characterised the exist- 
ing ones. Since the publication of that treatise a very material improve- 
ment has, we believe, taken place, — not only as regards the condition of 
societies already established, but the mode in which new ones have been 
constructed ; and we have thus the best evidence of the great utility of such 
works as that now before us. But in the present publication, Mr. Scratch- 
ley has greatly extended his original plan: whereas the former was con- 



— , or 14 years; at 4 per cent., in — , or 17-J- years, and so on; and this 



Reviews. 361 

fined to the consideration of Benefit Building Societies, Terminating and 
Permanent, their constitution and management, and to the investigation of 
the theories upon which they depend; the present treats, in addition, of 
Freehold Land Societies, Tontine Associations, Freehold Life Assurance, 
and Benefit Emigration and Colonization Societies; ample information 
being given as to the nature and constitution of each of them, and useful 
suggestions for their improvement and extension. In the Appendix the 
elementary propositions of the doctrine of Compound Interest are clearly 
laid down, and several theorems connected with the subject are also 
deduced, which are not less remarkable for their originality than their great 
practical utility. Thus it is shown at p. 243, that the number of years in 
which a sum of money will double itself at compound interest is, in round 
numbers, equal to the quotient of 70 divided by the rate of interest per 
cent, very nearly. So that at 5 per cent, a sum will become double in 

70 14 .a ♦ • 70 

— , or 14 years; at 4 per cent., in — . 

is a close approximation for all rates not exceeding 10 per cent. Again, 

. . •, , „*„ , 1 1 1.1 

it is demonstrated, at p. 257, that — — — = «, or — — ?=— -; and 

"n •"„ r„ A„ 

since we have tables at all rates of =-, or the annuities which £1 will 

purchase, we can obtain the annuity which will amount to £1 in n years 

by merely deducting the interest, and hence by simple inspection determine 

at once all the relations on which the value of any temporary investment 

depends. At a subsequent page, Mr. Scratchley shows that if a sum of 

money be borrowed for such a time, that it would amount at the expiration 

of it to /-fold its original value; then, the annuity which would pay it off, 

/ 
principal and interest in the same time, is equal to times one year's 

interest on the debt — a theorem of the utmost utility to building societies. 
Thus, in one of the ordinary kind, the monthly payment for the £60 share 
is readily found, by its means, to be ten shillings, or twice the interest for 
one month. 

But amongst its more minute features, nothing has struck us as more 
ingenious in Mr. Scratchley 's work than the demonstration at p. 294, 
that the value of a share in a tontine is independent altogether of the pro- 
bability of the life involved surviving to the time of division. This is a 
deduction sufficiently evident when pointed out, but one which would 
present itself at the first glance as extremely unlikely to be true. Our 
space will not admit of more particular allusion to the many other useful 
theorems contained in this part of the work; suffice it to say that the book 
is indispensable to building societies, and one which no association of a 
financial character should be without. To the student it will present many 
new problems, and many with which he is familiar, in a novel and instruc- 
tive point of view; whilst in some of the notes he will find matter to 
exercise analytical powers of no mean order.